Not quite. Society is still conflicted over whether prison is for punishment or rehabilitation. In the US, I think it trends mostly punishment with lip service to rehabilitation.
"Poorly" seems a bit harsh. From a conceptual standpoint, hospitals are, in some sense, a terrible idea: why would you want to concentrate contagious individuals (let along concentrate them in proximity to people with unrelated sicknesses). The only reason we have hospitals is the only way we can afford to provide medical care to the population.
According to the CDC, "On any given day, about one in 25 hospital patients has at least one healthcare-associated infection. "
